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Thank you, Charles, for providing this overview and glossary. It gives me a point of reference to look at your work with maybe some understanding. I've got a couple of questions, one general, and one specific. 

The general question concerns how to look up pieces. Several of us here have designed pieces, and might like to know how and where they fit into your scheme. I recognize some of Mats' pieces, I see George's Falcon family is there, and I even see Gavin Smith's planar pieces from Prince there. I think Larry Smith [no relation] played with planar pieces against Gavin, but Larry also did a rather thorough and extensive classification of Jetan pieces. It was Larry's monograph that made me realize how lucky I was not to have re-invented ERB's [and Larry's] pieces with some of my designs. So could I look up ERB's pieces, or my own pieces like the shaman or the flexible knight, in some systematic way? 

The second question is about planar pieces. Gavin and Larry seemed to agree [and I hope one or both will comment if I make a mistake] that planar pieces were 2D pieces that had to take every possible shortest path from their starting location to their ending location when they moved, and any single piece on a single one of those multiple locations making up all the shortest pathways from start to finish would block the move. I believe you also seem to accept their definition. I'd like to argue again [as I did with Larry, then], that this is far too restrictive a definition. 

Let's take a simple example of a planar rook and its target, an enemy planar bishop, 5 squares away diagonally, on the same 2D level/board section/whatever. Anyway, the planar rook can take the bishop if all 23 of the squares between the B and the R that occupy the 5x5 2D square [determined by using the positions of the B&R as opposite corners of the square] are empty, according to the rules. This is the weakest form of planar piece. [It's equivalent to damming a river by throwing a rock in it. To marginally mitigate this, there are 2 2D planes, and only 1 needs to be clear.] 

The strongest form of planar piece would be able to take if only one of all the shortest paths was open. An average planar piece might see the cut-off at half the paths available. A weakest cubic rook, B&R at opposite corners of a 5x5x5 cube, would require 123 empty cubes to capture the bishop. The bishop, being colorbound, would only need roughly half as many locations clear to effect a capture in general [and in the example given, only 3 empty cubes], thus more than overcoming its colorboundness to be worth more than the rook, no?

Those planar pieces which are not restricted by occupancy of their attack plane might actually be classified as 'hook-movers'.

The restriction of planar pieces might seem a little draconian, but only during the early portion of the game. As the field clears, these pieces begin to rise exponentially in threat.

A further restriction was developed because of the dynamics of the diagonal(and triagonal) planar piece. This was that all the cells within the planar move must exist on the field. Though developers and players are not strictly bond by this rule.

For a nice(or so I think) 2D game which demonstrates planar moves, try LiQi. It utilizes the same equipment as the Mad Queen(but it does not restrict the diagonal planar piece). There's also a Zillions implementation.

Thank you, Charles. I was intending to discuss the definition, with an interest in extending it a bit. I do see a possible need for expanded definitions [and a way to look up all pieces would be nice, even if all but impossible.] Planar pieces as used are just one step into area effect pieces - hook movers being another similar but different example, and the 2-step bent knightriders, especially [Jeremy's] with a ferz or wazir component, a third, shortrange version. Personally, I see a great need for some sort of organization of/within CVs. I'm happy there are people [crazy enough] um, willing to tackle it.   

I'd think planar pieces might be classified by how easy it is to block them, as a start. As pieces, they get more powerful the closer they are to their intended victim, an unusual phenomenon in chess, I suspect. This might be another sort of defining characteristic. I'd think they would be interesting pieces on very large boards, or greater than 2D boards. Which brings up the question of whether 'Planar' will be the stand-in [or the 'type specimen'] for planar, cubic, quatric, quintic... pieces. I'd say yes, at least for now. 

The more powerful versions of a planar piece would require more powerful versions of other pieces, or something such as a traffic cop piece, that slowed everything down, a la Roberto Lavieri's piece George mentioned recently, a somewhat less-than-Immobilizer. Or possibly some sort of reactive piece - Jeremy's Actualized Potential Pieces come to mind as a start for a piece that fires to a preset point or distance during the other player's turn, for example. Certainly, that piece would guard against the current planar pieces from 'behind' [but not 'directly' behind] the target piece. A 'battery' of these pieces might break up a major offensive in a larger [multimove, maybe] game. 

I guess the point of the previous paragraph is that once you've gotten the pieces to the board and used a bit, someone else will escalate. [Blue-sky fantasy desire: see all pieces cataloged in such a way that a designer who knew the system could look up newly-designed pieces to see if they are actually new, and what pieces are similar.] I'd think you'd want your system to be able to accomodate the pieces that will be showing up in the near future.